I'm in the middle of taking the free course on Special Relativity over on worldscienceu.com. I've already taken the simple version that doesn't include any math, and now I've just started the technical version that has all the math. It's a challenge since I haven't done complex math in years.
One of the things that I was already familiar with in relativity is how the EPR paradox kind of throws a challenge to the notion of the relativity of simultaneity. The EPR paradox is basically quantum entanglement. When two quantum particles become entangled, they can be separated at great distances and when one of the particles is measured and it becomes known that it has a certain spin, the other particle instantly becomes affected and will spin in the opposite direction. That won't become known until the other particle is measured of course, and any information about the spin of the first particle that was measured won't be able to travel faster than the speed of light. This seems to preserve Einstein's Special Relativity (SR) very well that no information can travel though space faster than light.
But this is not what bugs me. What bugs me is how if two distant particles can "instantly" affect one another, and if according to SR our reference frame that determines what is "now" depends on our velocity relative to other objects, how can the two entangled particles instantly affect one another? Suppose one of the particles was on a space ship travelling at 80% the speed of light and moving towards the other entangled particle that is a million light years away. According to SR the reference frame of the particle on the ship would require that its "now" slice contain the future events of the other distant particle. So if the particle on the moving ship is measured, does the other distant particle's spin change "instantly" or does it change in the far future, according to the measured particle's reference frame on the moving ship?